An electro-hydraulic brake system is described in SAE Paper 96/0991, where a braking request by the driver is derived from brake pedal activation by the driver. This braking request is converted into reference brake pressures for the individual wheel brakes, taking into consideration other operating variables. The reference brake pressures are established by pressure control circuits for each wheel, on the basis of the pre-determined reference brake pressure as well as the actual brake pressure measured in the area of the wheel brake. In such a hydraulic brake system, a reservoir is provided, which is charged by an electrically controlled pump for the pressure supply. In this connection, the pump is activated to charge the reservoir if the pressure in the reservoir goes below a certain value. For this purpose, a reservoir pressure sensor is provided, which detects the pressure in the pressure supply reservoir of the brake system. The reservoir pressure is also evaluated in connection with other functions of the brake system, for example, the pressure control circuits. If the reservoir pressure sensor fails, the system does not have a measurement value available for the reservoir pressure. The functions dependent on the reservoir pressure can therefore not be performed, or can only be performed in a greatly restricted manner.